Some other interesting series

The first such series we shall consider is the series generated by the formula 1/8(2x+1)^2 +7 This series generates a very similar series to the triangular number i.e the difference between consecutive terms is equal to 1m. Some terms are 1, 2 , 4 , 7, and so on… Indeed, if we subtract one we get the triangular numbers. Due to this coincidence, we can create another such formula for computing triangular numbers namely {1/8(2x+1)^2+7}-1.

Another such series is a series of numbers such that the difference of two consecutive odd number terms is equal to 2m. The formula for this is 1/4(2x+1)^2 +3. Some terms are 1, 3, 7, 13, 21, 31, and so on…

The last such series we will is a series of numbers such that the difference of any two consecutive number terms is equal to 7m. The formula for this is (2x+1)^2 +7)/8 + (2x+1)^2 +3)/4 + (2x+1)^2+1)/2.

Some terms of this are 3, 10, and 24.

All the formulas and series were discovered by me. Please attribute them to me if you are using these formulas.

Thank you,

Nunghead